In what follows we specialize to the derivation of \(p_{m=1,k}^{out}\)  first. The outage probability for arbitrary data stream \(m\)  can be got in an analogous way. By partitioning \({\bf {Z}}\)  as \({\bf {Z}} = [{{{\bf {z}}_1}},{{\bf {\tilde{Z}}}} ]\)  along with matrix inversion in block form in [1]}, \(p_{m{{ = }}1,k}^{out}\)  can be further expressed as
\(&p_{m=1,k}^{out} = \\&\quad \Pr \left[ {{{\bf {z}}_1}^{\rm {H}}\left( {{\bf {I}} - {\bf {\tilde{Z}}}{{\left( {{{{\bf {\tilde{Z}}}}^{\rm {H}}}{\bf {\tilde{Z}}}} \right)}^{ - 1}}{{{\bf {\tilde{Z}}}}^{\rm {H}}}} \right){{\bf {z}}_1} < \frac{1}{{{{\bar{\gamma }}}{\theta _{1,k}}\ell ({d_k})}}} \right].\) 
